In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.

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May 2020 For the Love of Mathematics Jokes

### Wayne Nirode

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

### Chris Harrow and Lillian Chin

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

### John H. Lamb

Vector properties and the birds' frictionless environment help students understand the mathematics behind the game.

### Jeremy S. Zelkowski

Do you always have to check your answers when solving a radical equation?

### Kasi C. Allen

A compelling contest motivates students and makes mathematics and STEM relevant.

### Sarah D. Ledford, Mary L. Garner, and Angela L. Teachey

Interesting solutions and ideas emerge when preservice and in-service teachers are asked a traditional algebra question in new ways.

### Maurice J. Burke

A tool that combines the power of computer algebra and traditional spreadsheets can greatly enhance the study of recursive processes.

### Christopher J. Bucher and Michael Todd Edwards

In the introductory geometry courses that we teach, students spend significant time proving geometric results. Students who conclude that angles are congruent because “they look that way” are reminded that visual information fails to provide conclusive mathematical evidence. Likewise, numerous examples suggesting a particular result should be viewed with skepticism. After all, unfore–seen counterexamples render seemingly valid conclusions false. Inductive reasoning, although useful for generating conjectures, does not replace proof as a means of verification.